Evaluate the definite integral. $\int^{-1}_{27}\left(-8\sqrt[3]{x}\right)\,dx = $
First, use the power rule: $\begin{aligned}\int^{-1}_{27}\left(-8\sqrt[3]{x}\right)\,dx~&=~\int^{-1}_{27}\left(-8x^\frac13\right)\,dx \\&=(-6x^\frac43)\Bigg|^{-1}_{{27}}\end{aligned}$ Second, plug in the limits of integration: $[-6\cdot({-1})^{\frac43}]-[-6\cdot{27}^{\frac43}] = -6+486= 480$. The answer: $\int^{-1}_{27}\left(-8\sqrt[3]{x}\right)\,dx~=~480$